The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.
The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.
Therefore, the correct answer is (2) the height from which the ball is thrown.
Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.
Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.
Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.
Therefore, option 2 is the correct answer.
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Solving absolute value equations
Solve4 (x+7)=16
Answer: X = -3
Step-by-step explanation:
The question is in the photo!
The answer is A. The game is strictly determined and the value of the game is -7.
What is matrix?A rectangular array of characters, numbers, or phrases arranged in rows and columns is known as a matrix.
Given matrix, where we have to find out, is the game strictly determined for the following matrix or not?
[tex]\left[\begin{array}{ccc}-7&7&-3\\3&8&6\\1&3&-3\end{array}\right][/tex]
Using the minimax theorem, we know that if the game is strictly determined, the value of the game is equal to the value of the saddle point. If the game is not strictly determined, the value of the game may not exist or may be a range of values.
We can check each row and column for minimum and maximum values:
The minimum value in the first row is -7.
The maximum value in the second column is 7.
The minimum value in the third row is -3.
We can see that the element in the first row and second column is both the minimum in its row (-7) and the maximum in its column (7), so it is a saddle point. Therefore, the game is strictly determined and the value of the game is -7.
The answer is A. The game is strictly determined and the value of the game is -7.
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the time taken to fill a tank was 2 hours and 43 minutes. write this time to the nearest 5 minutes
Answer:
To write the time taken to fill a tank to the nearest 5 minutes, we first need to convert 2 hours and 43 minutes to minutes. 2 hours = 2 x 60 = 120 minutes So, the total time taken in minutes is: 120 + 43 = 163 minutes To round this to the nearest 5 minutes, we need to consider the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down to the nearest multiple of 5, which is 160. Therefore, the time taken to fill the tank to the nearest 5 minutes is: 2 hours and 43 minutes = 160 minutes = 2 hours and 40 minutes
To write the given time to the nearest 5 minutes, round down the minutes value if the last digit is less than 5, and keep the hours value as it is.
Explanation:To write the given time to the nearest 5 minutes, we need to round it to the closest multiple of 5. The given time is 2 hours and 43 minutes. To round to the nearest 5 minutes, we look at the last digit of the number of minutes, which is 3. Since 3 is less than 5, we round down the minutes to 0 and keep the hours as it is. Therefore, the time to the nearest 5 minutes is 2 hours and 40 minutes.
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Question
Find the product.
(3x2+x−2)(−4x2−2x−1)=
Answer:
-12x⁴-10x³+3x²+3x+2
Step-by-step explanation:
(3x²+x−2)(−4x²−2x−1)=3x²(−4x²−2x−1)+x(−4x²−2x−1)−2(−4x²−2x−1)
{ ( a+b ) ( a+b )=a ( a+b )+b ( a+b ) by distributive property }
= -12x⁴-6x³-3x²-4x³-2x²-x+8x²+4x+2
= -12x⁴-10x³+3x²+3x+2
What is the correct shortcut?
The triangle congruence postulate used for the given diagram is; SSS
How to find the triangle congruence postulate?There are different triangle congruency postulates namely:
SSS: Side Side Side Congruency Postulate
SAS: Side Angle Side Congruency Postulate
ASA: Angle Side Angle Congruency Postulate
AAS: Angle Angle Side Congruency Postulate
HL: Hypotenuse Leg Congruency Postulate
From the given image, we see that we see that we have three congruent sides shown of both triangles and as such the triangles are congruent by SSS Congruency Postulate.
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Determine the value of x.
A) 5/3
B) 10
C)5
D) 10/3
Check the picture below.
The length of the hypotenuse (x) in the given right triangle is approximately 10 units.
Hence the correct option is B.
Given is right triangle with perpendicular side having measurement of 5 units,
The acute angle between the base and the hypotenuse = 30°
The acute angle between the perpendicular and the hypotenuse = 60°
We need to find the length of the hypotenuse (x).
We can use the trigonometric ratio for sine (sin) to relate the lengths of the sides.
In this case, we'll use the sine of the 30° angle:
sin(30°) = opposite/hypotenuse
sin(30°) = 5/x
To solve for x, we can rearrange the equation:
xsin(30°) = 5
x = 5 / sin(30°)
Now, we can calculate the value of x using this equation:
x = 5 / sin(30°)
x ≈ 10 units
Therefore, the length of the hypotenuse (x) in the given right triangle is approximately 10 units.
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A retailer sold bat at 25% profit. Cost price of 5 bats is equal to cost price of 4 balls. On ball retailer earns 40% profit. If on selling one bat and one ball he earns Rs. 45 profit then find cost price of ball
The cost price of one ball is equal to Rs. 75
How to evaluate for the cost price of ballWe shall represent the cost price of one bat with the letter 'x', so that the selling price of one bat is 125% of 'x', which is 1.25x.
The cost price of 5 bats is equal to the cost price of 4 balls. So,
5x = 4y, where 'y' is the cost price of one ball.
y = (5/4)x
Also, we know that the profit percentage on one ball is 40%. So, the selling price of one ball is 140% of its cost price, which is 1.4y.
Profit earned on selling one bat and one ball is calculated as:
Profit = Selling price - Cost price
Profit = (1.25x + 1.4y) - (x + y)
Profit = 0.25x + 0.4y
Profit = 0.25x + 0.4(5/4)x {Substituting the value of 'y'}
Profit = 0.75x
given that the above profit is equal to Rs. 45. them,
0.75x = 45
x = 60
The cost price of one bat is Rs. 60 and the cost price of one ball:
y = (5/4)x
y = (5/4) × 60
y = 75
Therefore, the cost price of one ball is Rs. 75.
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Reflect -8,-5 across the x-axis.
Then reflect the result across the y-axis.
what are the coordinates of the final point?
Its not on a graph thats why i dont know
The final point after both reflections would be (8, 5).
what is a graph?
A graph is a visual representation of data, typically in the form of a diagram or chart, used to show the relationship between different variables or quantities. Graphs are commonly used to display data in a way that makes it easier to understand and analyze.
Graphs can take many different forms, depending on the type of data being presented and the purpose of the graph. Some common types of graphs include:
Line graphs: Used to show trends over time.
Bar graphs: Used to compare different values or quantities.
Pie charts: Used to show the proportion of different components of a whole.
Scatter plots: Used to show the relationship between two variables.
Histograms: Used to show the frequency distribution of a set of data.
To reflect a point across the x-axis, we simply change the sign of the y-coordinate. So if we start with the point (-8, -5), its reflection across the x-axis would be (−8, 5).
To reflect a point across the y-axis, we change the sign of the x-coordinate. So reflecting the point (−8, 5) across the y-axis would give us (8, 5).
Therefore, the final point after both reflections would be (8, 5).
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5. James Rodriguez strikes a soccer ball during penalty kicks. The arc of the ball can be mapped by the function f(x) = −8t(t – 8). How long does the ball spend in the air?
Answer:
The function f(x) = -8t(t - 8) represents the height of the soccer ball at any given time t, where t is the time in seconds after the ball was kicked.
To find out how long the ball spends in the air, we need to determine the time at which the ball hits the ground. The ball hits the ground when its height is zero, so we can set f(x) = 0 and solve for t:
-8t(t - 8) = 0
This equation has two solutions: t = 0 and t = 8. The first solution corresponds to the time when the ball is kicked and the second solution corresponds to the time when the ball hits the ground. Since we're interested in the time the ball spends in the air, we need to subtract the time the ball was kicked from the time the ball hits the ground:
t = 8 - 0 = 8 seconds
Therefore, the ball spends 8 seconds in the air.
Please help wwaaaaaaaa
The recursive formula for the given sequence is:
f(n) = f(n - 1) + 3
How to write a recursive formula for the sequence?Here we have the graph of a sequence, we can see that the first terms are:
f(0) = 4
f(1) = 7
f(2) = 10
f(3) = 13
f(4) = 16
A recursive formula tells us how to find the value of the n-th term of the sequence by using the previous terms.
By looking at the values above, you can see that all the terms are 3 units apart, so the recursive sequence that we can use here is:
f(n) = f(n - 1) + 3
It says that "the n-th term is equal to the previous term plus 3"
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a questionnaire that can help advise a person whether to take a gap year or not
Answer:
What are your goals for taking a gap year?
Are you looking to gain new experiences, skills, or perspectives?
Do you want to travel, learn a new language, or volunteer?
Are you trying to improve your mental health or overall well-being?
What are your current academic or career plans?
Do you have a clear idea of what you want to study or what career you want to pursue?
Have you already been accepted into a program or job?
What are your financial circumstances?
Can you afford to take a gap year without negatively impacting your future plans?
Do you have savings or a plan to work during your gap year?
How will taking a gap year affect your relationships with friends and family?
Will you be able to stay in touch with loved ones while you're away?
Will you miss any important events or milestones?
What are the potential risks and rewards of taking a gap year?
Could it delay your academic or career goals?
Could it help you gain valuable experience or clarity about your future plans?
How do you feel about the idea of taking a gap year?
Are you excited about the possibilities, or do you feel uncertain or anxious?
By answering these questions honestly, you should have a better idea of whether taking a gap year is the right decision for you. Keep in mind that there is no one-size-fits-all answer, and what works for one person may not work for another. Ultimately, the decision should be based on your own unique goals, circumstances, and desires.
Step-by-step explanation:
Alfred is y years old
Libby is 4 years younger
than Alfred.
John is 4 times as old as
Libby.
Write down an expression in terms of y, for john’s age.
Answer:
therefore, the expression for John's age in terms of y is 4y - 16.
Step-by-step explanation:
Answer:
John's age = 4y - 16
Step-by-step explanation:
We can start by using the information given to write expressions for the ages of Libby and John in terms of Alfred's age y.
We know that Libby is 4 years younger than Alfred, so her age can be written as:
Libby's age = Alfred's age - 4
We also know that John is 4 times as old as Libby, so his age can be written as:
John's age = 4 × Libby's age
Substituting the expression for Libby's age from the first equation into the second equation, we get:
John's age = 4 × (Alfred's age - 4)
Simplifying this expression, we get:
John's age = 4 × Alfred's age - 16
Therefore, an expression in terms of y for John's age is:
John's age = 4y - 16
Write the first four terms of a maclaurin series for f(x) = e^x
On solving the question we have that the answer of the equation will be [tex]Answer: "f(x) = 1 + x +\frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
What is equation?A math equation is a mechanism for connecting two statements and indicating equivalence with the equals sign (=). To explain the connection between the two sentences put on each side of a letter, a statistical method can be employed. The software and the logo are usually interchangeable. 2x - 4 equals 2, for example. An equation is a logical expression that asserts the equality of some mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14.
[tex]"f(x) = {e^x} \Rightarrow f'(x) = {e^x} \Rightarrow f''(x) = {e^x} \Rightarrow f'''(x) = {e^x}"[/tex]
Then
[tex]"f(x) = f(0) + \frac{{f'(0)}}{{1!}}x + \frac{{f''(0)}}{{2!}}{x^2} + \frac{{f'''(0)}}{{3!}}{x^3} + ... = {e^0} + \frac{{{e^0}}}{1}x + \frac{{{e^0}}}{2}{x^2} + \frac{{{e^0}}}{6}{x^3} + ... = 1 + x + \frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
[tex]Answer: "f(x) = 1 + x + \frac{1}{2}{x^2} + \frac{1}{6}{x^3} + ..."[/tex]
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Consider the following equation.
−7y+5x=5(−7+x)
Step 2 of 2: Graph the equation by plotting the x- and y-intercepts. If an intercept does not exist, or is duplicated, use another point on the line to plot the graph.
The graph οf the equatiοn −7y + 5x = 5(−7 + x) is a straight line passing thrοugh the pοint (0, 5) with a negative slοpe.
What is Linear Equatiοn in Twο Variables?A linear equatiοn in twο variables is an equatiοn that can be written in the fοrm ax + by = c, where a, b, and c are cοnstants and x and y are variables.
Tο graph the equatiοn −7y + 5x = 5(−7 + x), we can first find the x- and y-intercepts by setting each variable tο zerο in turn.
When y = 0, we get:
-7y + 5x = 5(-7 + x)
0 + 5x = 5(-7 + x)
5x = -35 + 5x
0 = -35
This is a cοntradictiοn, which means that there is nο x-intercept.
When x = 0, we get:
-7y + 5x = 5(-7 + x)
-7y + 0 = 5(-7 + 0)
-7y = -35
y = 5
Sο the y-intercept is (0, 5).
Therefοre, the graph οf the equatiοn −7y + 5x = 5(−7 + x) is a straight line passing thrοugh the pοint (0, 5) with a negative slοpe.
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Estimated Salary=29,608.40+2632.98(Years of Experience)
What is the estimated salary for an employee with 18
years of experience?
The estimated salary fοr an emplοyee with 18 years οf experience is $77,201.24.
What is BODMAS?BODMAS stands fοr Brackets, Order, Divisiοn/Multiplicatiοn, Additiοn/Subtractiοn, and it represents the οrder οf mathematical οperatiοns tο be perfοrmed when evaluating an expressiοn. It ensures that expressiοns are evaluated in a cοnsistent and unambiguοus manner.
Tο calculate the estimated salary fοr an emplοyee with 18 years οf experience using the prοvided fοrmula, we can substitute 18 fοr "Years οf Experience" and sοlve fοr the salary:
Estimated Salary = 29,608.40 + 2632.98(18)
Estimated Salary = 29,608.40 + 47,592.84
Estimated Salary = 77,201.24
Therefοre, the estimated salary fοr an emplοyee with 18 years οf experience is $77,201.24.
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Kremena took out a $500 discounted loan for a period of 3 months. The amount she actually received into her bank account was $460. Assuming simple interest rates, what is effective interest rate re?
The effective interest rate on the loan is also 32%.
What is effective interest rate ?
Effective interest rate is the actual interest rate that is paid or earned on an investment, loan, or other financial product. It takes into account not only the nominal interest rate, which is the stated rate of interest, but also the frequency of compounding or other factors that affect the overall return.
According to the question:
To find the effective interest rate, we first need to calculate the amount of interest Kremena paid on the loan. We can do this by subtracting the amount she received from the amount of the loan:
Interest = Loan amount - Amount received
Interest = $500 - $460
Interest = $40
Next, we can use the formula for simple interest to calculate the interest rate:
I = P * r * t
where I is the interest, P is the principal (loan amount), r is the interest rate, and t is the time in years.
Since Kremena took out the loan for 3 months, which is a quarter of a year, we have:
I = P * r * t
$40 = $500 * r * (3/12)
$40 = $500 * r * 0.25
r = $40 / ($500 * 0.25)
r = 0.32 or 32%
So the interest rate on the loan is 32%. However, this is the nominal interest rate, which does not take into account the effects of compounding. To find the effective interest rate, we need to take into account the fact that Kremena only received $460, which means that she effectively paid more interest than she would have if she had received the full $500.
To calculate the effective interest rate, we can use the formula:
[tex]re = (1 + r/n)^n - 1[/tex]
where re is the effective interest rate, r is the nominal interest rate, and n is the number of compounding periods per year. Since the problem specifies simple interest, there is no compounding, so we can take n = 1. Plugging in the values, we get:
[tex]re = (1 + 0.32/1)^1 - 1[/tex]
re = 0.32 or 32%
So the effective interest rate on the loan is also 32%.
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Solving Square Root Equations
Solve the following equations. Be sure to label any extraneous solutions.
The solution of each equation are;
1) x = 6, x = 0
2) x = 3, x = 2
3) x= 4 ±√6
4) x = 6 ± √24/2
What is an extraneous solution?An extraneous solution is a solution obtained in a mathematical equation that does not satisfy the original equation, even though it appears to be a valid solution when plugged into the equation.
1) (√6x)^2 = x^2
6x = x^2
x^2 - 6x = 0
x = 6, x = 0
2) √5x - 6 = x
5x - 6 = x^2
x^2 - 5x + 6 = 0
x = 3, x = 2
3) √2x - 1 = x - 3
2x - 1 = (x - 3)^2
2x - 1 = x^2 - 6x + 9
x^2 - 6x - 2x + 9 + 1 = 0
x^2 -8x + 10 = 0
x= 4 ±√6
4) x = 2 + √2x - 11
x -2 = √2x - 11
x^2 - 4x + 4 = 2x - 11
x^2 -4x -2x + 4 + 11 = 0
x^2 - 6x + 15 = 0
x = 6 ± √24/2
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What is 15 rounded to the nearest hundred
Answer:600
Step-by-step explanation:
Since this number is less than 5, we round down the number, i.e. we round it off to the nearest 100 that comes next to this number. So, 15 becomes 00 which on adding to 6 at the hundred's places, becomes 600.
At her Fourth of July party, Lexi serves her famous grilled chicken. Her secret is to use 6 fluid ounces of lemon-garlic marinade for every pound of chicken. Lexi plans to grill 4 pounds of chicken. How many cups of marinade should she use? cups
What is the value of x?
Answer:
x = 26 degrees
Step-by-step explanation:
Supplementary angles mean that they sum up to be 180 degrees therefore
C + D = 180 degrees
128 degrees + D = 180 degrees
D = 180 degrees - 128 degrees
D = 52 degrees
If the measure of the angle D is two times the value of x then x is...
x = D/2
x = 52 degrees / 2
x = 26 degrees
If the total amount of wealth in the world is $418.3 Trillion, and the wealth of the top 1% combined is worth more than $190 Trillion, what percent of global wealth is concentrated in the hands of the top 1%
?
Answer: The top 1% of the world's population holds more than 45% of global wealth.
Step-by-step explanation:
To find the percentage of global wealth concentrated in the hands of the top 1%, we need to divide the wealth of the top 1% by the total amount of global wealth, and then multiply by 100 to get the percentage.
Percentage of global wealth held by top 1% = (Wealth of top 1% / Total global wealth) x 100
We are given that the total amount of global wealth is $418.3 trillion, and the wealth of the top 1% is more than $190 trillion.
So, the percentage of global wealth held by the top 1% is:
(190 trillion / 418.3 trillion) x 100 = 45.38%
Therefore, the top 1% of the world's population holds more than 45% of global wealth.
Answer:
45.42%
Step-by-step explanation:
To find:-
What percent of global wealth is concentrated in the hands of the top 1% .Answer:-
We are here given that, the total global wealth is 418.3T dollars and more than 190T dollars is in hands of top 1% of the people. We are interested in finding out the percentage of global wealth in the hands of top 1% . We can find the percentage as ,
[tex]:\sf\implies \pink{ \% =\dfrac{Wealth\ owned\ by \ 1\% }{Total\ wealth}\times 100}\\[/tex]
On substituting the respective values, we have;
[tex]:\sf\implies \% =\dfrac{\$ 190T}{\$ 418.3T}\times 100\\[/tex]
[tex]:\sf\implies \pink{\% = 45.42\% } \\[/tex]
Hence the required percentage is 45.42% .
Lindsey estimated the amount of liquid in a container to be 80 ml. The actual amount of liquid was 83 ml. What is the percent error? Round your answer to the nearest whole percent.
If two adjacent angles (x+18) and x are inside a 90° angle, what is the equation for the two adjacent angles?
Answer:
Step-by-step explanation:
For a right angle triangle we use Pythagoras theorem
hypotenuse²=x²+(x+18)²
=x²+x²+36x+324
=2x²+36x+324
Circle O shown below has a radius of 20 inches. Find, to the nearest tenth,
the radian measure of the angle, x, that forms an arc whose length is 38
inches.
The radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.
What is an angle ?
The length of an arc of a circle is given by the formula:
length of arc = radius * angle in radians
Let x be the radian measure of the angle that forms an arc of length 38 inches in Circle O. Then we can write:
38 = 20x
Solving for x, we get:
x = 38/20
x = 1.9 radians (to the nearest tenth)
Therefore, the radian measure of the angle that forms an arc of length 38 inches in Circle O is approximately 1.9 radians.
What is an arc?
In geometry, an arc is a segment of a curve, such as a circle or an ellipse. It is defined as the portion of the curve that lies between two distinct endpoints. An arc is named based on its endpoints, and it can be classified as a minor arc, major arc, or semicircle depending on its length. A minor arc is an arc that measures less than 180°, a major arc is an arc that measures more than 180°, and a semicircle is an arc that measures exactly 180°. The measure of an arc is typically given in degrees or radians, and it can be calculated using the formula:
measure of arc = (central angle/360) * 2πr
where r is the radius of the circle, and the central angle is the angle that the arc subtends at the center of the circle.
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Help quickly!! 100 POINTS NEEDED QUICKLY
A two-digit locker combination has two nonzero digits and no two digits are the same. Event A is defined as choosing an odd digit for the first number, and event B is defined as choosing an even digit for the second number.
If a combination is picked at random, with each possible locker combination being equally likely, what is P(B|A) expressed in simplest form?
The conditional probability is given as follows:
P(B|A) = 1/2, option C.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The events are given as follows:
Event A: odd digit for the first number.Event B: even digit for the second number.P(B|A) is the probability that the second digit is even, considering that the first digit was odd. As the digits cannot repeat, and there will be 8 remaining digits, out of which 4 will be even, the probability is given as follows:
P(B|A) = 4/8 = 1/2.
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PLEASE HELP WILL GIVE BRAINLISET AND 60 PTS I APPRECIATE IT !!:)
Answer:
Step-by-step explanation:
domain is negative infinity, positive infinity
range is -3, positive infinity
Answer:
F(x) is all values that x can be. so the answer is the domain is (-∞,4)
Step-by-step explanation:
Find the savings plan balance after 6 months with an APR of 2% and monthly payments of $150.
www
The balance is $.
(Do not round until the final answer. Then round to the nearest cent as needed.)
The savings plan balance after 6 months with an APR of 2% and monthly payments of $150 is approximately $913.35.
What distinguishes nominal interest rates from effective interest rates?The stated interest rate on a loan or investment is known as the nominal interest rate; it does not account for compounding or any other elements that may have an impact on the real return or expense. Often, it is stated as an annual percentage rate (APR).
The effective interest rate, in contrast, takes into account compounding and other elements that may have an impact on the true cost or return of a loan or investment. It is often represented as an annual percentage yield and represents the actual rate of return or cost that is earned or paid on the principal amount over a certain time (APY).
Given that,
APR = 2% and monthly payments = $150.
For future value of annuity we use the following formula:
FV = Pmt × [(1 + r)⁽ⁿ⁻¹⁾] /r
Substituting the values:
r = 0.02/12 = 0.0016667, n = 6, and Pmt = $150:
FV = $150 × [(1 + 0.0016667)⁽⁶⁻¹⁾]/0.0016667
FV ≈ $913.35
Hence, the savings plan balance after 6 months with an APR of 2% and monthly payments of $150 is approximately $913.35.
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Solve the system
y=3x+1
-x+2y=-3
Therefore , the solution of the given problem of equation comes out to be x = -14/15 and y = -37/15 .
What is an equation?It is standard practise in mathematical formulas to employ a single variable term to ensure agreement between competing claims. Equations, which are mathematical statements, are used to demonstrate the equality of many academic integers numbers. Instead of dividing 12 into 2 parts in this instance, the normalise technique adds b + 6 to use the data from y + 6.
Here,
We can use the substitution or elimination technique to solve this system. Here, we'll employ the removal strategy.
given solution system:
=> y = 3x + 1 (1)
=>-x + 2y = -3 (2) (2)
By combining equations (1) and (2) multiplied by 1 and 3, respectively, we can remove the variable x:
=>3*(-x + 2y = -3)
=> -3x + 6y = -9
=> 1*(y = 3x + 1)
=> y = 3x + 1
Combining the two equations:
=>y = 3x + 1
=> -3x + 6y = -9
=> 6y - 3x = -8
By multiplying both parts of this equation by 3, we can make it simpler:
=> 2y - x = -8/3
However, we can still use equation (1) to replace y even though we have a new equation in terms of x and y:
=> y = 3x + 1
=> 2y - x = -8/3
y = 3x Plus 1 is substituted in the second equation:
=>2(3x + 1) - x = -8/3
=> 6x + 2 - x = -8/3
=>5x = -14/3
=>x = -14/15
Finding y by substituting this x number in equation (1):
=> y = 3x + 1 = 3(-14/15) + 1 = -37/15
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i need help with question 9
Answer:
Option D
Step-by-step explanation:
Total number of posters Rhett puts up = 9
Printing cost of each poster = $2
∴Total cost on posters = ([tex]\frac{2 dollars}{1 poster}[/tex]) × (9 posters)
= $18
Note: The unit multiplier used above is arranged in a way that the current unit of “posters” is cancelled out and the answer is assigned with the new unit of “dollars".
Number of fliers Rhett gives out = x
Printing cost of each flier = $0.20
∴Total cost on fliers = [tex]\frac{0.20 dollars}{1flier}[/tex] × (x fliers)
= $0.20x
Note: The unit multiplier used above is arranged in a way that the current unit of “fliers” is cancelled out and the answer is assigned with the new unit of “dollars”
∴How much it cost Rhett to search for his lost puppy:
y = Total cost on fliers + Total cost on posters
∴[tex]y = 0.20x + 18[/tex]
∴Option D
DEDUCTION AND APPLICATION Do not use a calculator when answering Part 3. 3.1 Apply the compound angle expansion sin(x + y) = sin x cos y + cos x sin y to expa sin 2x and simplify your answer: sin 2x = sin(x+x) 3.2 Expand each of the following, using your answer from 3.1: 3.2.1 sin 100° = ..... 3.2.2 sin 46° = .... 3.2.3 sin 40° =. Write the following expressions as a single trigonometric ratio: 3.3.1 2 sin 19° cos 19° = 3.3.2 2 cos 40° sin 40° - 3.3.3 sin 25° cos155° .........
Answer:
Step-by-step explanation:
3.1:
Using the compound angle expansion, we have:
sin 2x = sin(x + x) = sin x cos x + cos x sin x
sin 2x = 2 sin x cos x
Therefore, sin 2x = 2 sin x cos x.
3.2:
Using the result from 3.1:
3.2.1: sin 100° = 2 sin 50° cos 50° = sin 100° = 0.766
3.2.2: sin 46° = 2 sin 23° cos 23° = sin 46° = 0.719
3.2.3: sin 40° = 2 sin 20° cos 20° = sin 40° = 0.642
3.3:
Using the identity sin(a ± b) = sin a cos b ± cos a sin b:
3.3.1: 2 sin 19° cos 19° = sin 38° = sin (45° - 7°) = sin 45° cos 7° - cos 45° sin 7° = (1/√2)cos 7° - (1/√2)sin 7° = -sin (7° - 45°) = -sin 38°
Therefore, 2 sin 19° cos 19° = -sin 38°.
3.3.2: 2 cos 40° sin 40° = sin 80° = sin (45° + 35°) = sin 45° cos 35° + cos 45° sin 35° = (1/√2)cos 35° + (1/√2)sin 35° = sin (35° + 45°) = sin 80°
Therefore, 2 cos 40° sin 40° = sin 80°.
3.3.3: sin 25° cos 155° = (1/2)(sin 180°) = 0
Therefore, sin 25° cos 155° = 0.